Optimal linear combination of sensors and actuators to enforce an interior conic open‐loop system

Abstract

SummaryThis paper presents techniques to linearly combine the sensor measurements and/or actuator inputs of a linear time‐invariant system to obtain a new system that is interior conic with prescribed bounds. In the optimal sensor combination problem, a desired system output is defined, and in the optimal actuator combination problem, a desired system input is defined, along with a frequency bandwidth in which the desired system input or output should be matched. The simultaneous optimal sensor and actuator combination problem includes desired system outputs and inputs. In all cases, the weighted or norm of the difference between the system with linearly combined sensors or actuators and the desired system is minimized while rendering the new system interior conic with prescribed bounds. The weighting transfer matrix used in the ‐ or ‐optimization problem is determined by the frequency bandwidth of interest. The individual sensor and actuator combination methods involve linear matrix inequality constraints and are posed as convex optimization problems, whereas the combined sensor and actuator method is an iterative procedure composed of convex optimization steps. Numerical examples illustrate superior tracking performance with the proposed sensor and actuator combination techniques over comparable techniques in the literature when implemented with a simple feedback controller. Robust asymptotic stability of the closed‐loop system to plant uncertainty is demonstrated in the numerical examples.